Problem: Two 6-sided dice, one red and one green, are rolled.  What is the probability that the red die shows an odd number and the green die shows a number that is a perfect square?
Solution: As per most two-die problems, the total number of outcomes is 36.  So now we need to calculate the number of successful outcomes.  There are 3 successful outcomes for the red die: it must show 1, 3, or 5.  There are 2 successful outcomes for the green die: it must show 1 or 4.  Since the rollings of the two dice are independent events, to get to number of successful outcomes for both dice, we multiply the counts for each die, so the number of successful outcomes is $3 \times 2 = 6$.  Therefore, the probability of success is $\frac{6}{36} = \boxed{\frac16}$.